NewYork-Presbyterian has resolved a monthslong contract dispute with the insurer Healthfirst, allowing the hospital system to remain in-network for some 2 million New Yorkers with coverage through the nonprofit. The agreement, confirmed Tuesday by the hospital and the insurer, is welcome news to patients throughout the region. As of Tuesday morning, NewYork-Presbyterian’s website had been updated to inform patients with Healthfirst insurance that their care would continue to be covered after that date. “We are pleased to share that NewYork-Presbyterian has reached an agreement with Healthfirst,” the hospital network posted online. Healthfirst initially stirred panic among some patients over the summer when the insurer announced that NewYork-Presbyterian had abruptly canceled a multiyear contract prematurely.